## Question 5:

### Part (i):
| Answer | Mark | Guidance |
|--------|------|----------|
| Refer to translation and stretch | M1 | In either order; ignore details here; allow any equiv wording (such as move or shift for translation) to describe geometrical transformation but not statements such as add 3 to $x$ |
| **Either:** State translation in negative $x$-direction by 3 | A1 | Or state translation by $\begin{pmatrix}-3\\0\end{pmatrix}$; accept horizontal to indicate direction; term 'translate' or 'translation' needed for award of A1 |
| State stretch by factor 2 in $y$-direction | A1 | Or parallel to $y$-axis or vertically; term 'stretch' needed for award of A1; these two transformations can be given in either order. SC: if M0 but details of one transformation correct, award B1 for 1/3 (in Either, Or 1, Or 2 cases) |
| **Or 1:** State stretch by factor $\frac{1}{2}$ in $x$-direction | A1 | Or parallel to $x$-axis; term 'stretch' needed for award of A1 |
| State translation in negative $x$-direction by 3 | A1 | Or state translation by $\begin{pmatrix}-3\\0\end{pmatrix}$; term 'translate' or 'translation' needed; these two transformations must be in this order – if details correct for M1A1A1 but order wrong, award M1A1A0 |
| **Or 2:** State translation in negative $x$-direction by 6 | A1 | Or state translation by $\begin{pmatrix}-6\\0\end{pmatrix}$; term 'translate' or 'translation' needed |
| State stretch by factor $\frac{1}{2}$ in $x$-direction | A1 | Or parallel to $x$-axis; term 'stretch' needed for award of A1; these two transformations must be in this order – if details correct for M1A1A1 but order wrong, award M1A1A0 |

### Part (ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| **Either:** Solve linear eqn/ineq to obtain critical value $-6$ | B1 | |
| Attempt solution of linear eqn/ineq where signs of $x$ and $2x$ are different | M1 | |
| Obtain critical value $-2$ | A1 | |
| Attempt solution of inequality | M1 | Using table, sketch, …; implied by correct answer or answer of form $a<x<b$ or of form $x<a, x>b$ (where $a<b$); allow $\leq$ here |
| Obtain $-6 < x < -2$ | A1 | As final answer; must be $<$ not $\leq$; allow "$x>-6$ and $x<-2$" |
| **Or:** Square both sides to obtain $x^2 > 4(x^2+6x+9)$ | B1 | Or equiv |
| Attempt solution of 3-term quadratic eqn/ineq | M1 | With same guidelines as in Q2(ii) for factorising and formula |
| Obtain critical values $-6$ and $-2$ | A1 | |
| Attempt solution of inequality | M1 | Using table, sketch, …; implied by correct answer or answer of form $a<x<b$ or of form $x<a, x>b$ (where $a<b$); allow $\leq$ here |
| Obtain $-6 < x < -2$ | A1 | As final answer; must be $<$ not $\leq$; allow "$x>-6$ and $x<-2$" |

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